A Liouville type theorem for non-linear elliptic systems involving advection terms. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Duong, Anh Tuan
• Is Part Of: Complex variables and elliptic equations. Volume 63:Issue 12(2018)
• Page Start: 1704
• Page End: 1720
• Publication Date: 2018-12-02
• Subjects: Liouville-type theorem -- advection terms -- stable solutions -- elliptic systems; Primary: 35B53 -- 35J60 -- Secondary: 35B35 -- 35J70; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2017.1403427
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract: In this paper, we study the following elliptic system where a is a smooth divergence-free vector field satisfying some decay condition and . We establish a Liouville type result for stable positive solutions of the system in the case and . In particular, when, our result is a natural extension of Cowan [Nonlinear Anal. 2014;104:1–11] to the equation with advection.